Shock-boundary layer interactions (SBLIs) are ubiquitous occurrences in supersonic and
hypersonic vehicles and have the tendency to inhibit their structural and aerodynamic performance.
For example, in the inlets and isolators of such vehicles, the shock wave generated
by one surface interacts with the boundary layer on an adjacent one. They are also present
on the exterior of the vehicles, e.g. at the fuselage/vertical stabilizer junctions. These interactions
cause unsteady separation, resulting in reduced air in-take efficiency, or unstart
in extreme cases; unsteady vortex shedding which yields undesirable broadband noise; and
significant pressure fluctuations which compromise the structural integrity of the vehicle and
which can lead to loss of control authority. Mitigating these issues is therefore an important
part of optimizing aerodynamic and structural design of high speed vehicles. The first step
in this respect is obtaining a better understanding of the interaction unsteadiness.
Nominally 2-D interactions have been studied extensively and have identified low-frequency
shock motions which lead to undesirable pressure loads. The particular frequencies associated
with the motions have been characterized using time resolved experiments and computations,
and shown to depend on the mean size of the separation. The physical processes responsible
for these frequencies are however still under investigation and the physical relationship
between the shock motions and pulsations of the separation bubble remains obscure.
For flow fields where the shock is swept, a complex 3-D interaction is encountered whose
unsteady features are even less well understood. The mean structure of these 3-D interactions
has been obtained experimentally and using RANS simulations, and shown to be profoundly different from the 2-D flow field indicating that progress in understanding 2-D interactions
cannot be directly translated to 3-D. Specifically, there is no recirculating region in the 3-D
interaction contrasting with the 2-D case where a closed separation bubble essentially drives
the dynamics. This effort seeks to understand the unsteadiness in such 3-D interactions.
Although Large Eddy Simulations (LES) are invaluable for characterizing time evolving
features, they are prohibitively expensive for swept interactions. A stability analysis
based method, the Mean Flow Perturbation (MFP) technique appears as a better alternative
to LES in terms of computational cost. It involves tracking the evolution of disturbances
through the interaction in space and time to identify the low frequency and stability properties
of the chaotic 3-D dynamical system.
A systematic verification and validation of the technique is presented to provide a solid
basis for its employment. By implementing the technique on canonical problems with similar
properties as the swept interaction, its applicability for flows with strong gradients and
viscous effects is established. The method is then implemented on the simpler 2-D interaction
with two specific goals: to ensure that MFP accurately captures well known unsteady features
of the flow and to learn relevant lessons and establish best practices for SBLI application.
By definition, the implementation of MFP requires the knowledge of a mean base state.
For the nominally 2-D interactions, the mean of a previously obtained LES is used as the
basis. In addition to providing the input to the MFP technique, the LES is used as a testbed
to: (i) Improve effectiveness of a technique for generating spatially developing supersonic
turbulent boundary layers (TBLs) as correctly characterizing the inflow boundary condition
is a critical component of simulating SBLIs. (ii) Generate insight on possible physical mechanisms
responsible for the low frequency unsteadiness in 2-D by exploiting asymmetry in the
shock motions.
Besides the LES supplied mean base state, the MFP technique is also implemented with
a RANS supplied base flow. No significant differences in the results are observed indicating
a relative independence of the MFP technique to the base flow generation procedure. Due to
the highly prohibitive nature of implementing LES for 3-D interactions, the above observation
acts as a substantial endorsement for using RANS generated base state for studying 3-D
interactions with the MFP technique. It also provides specific insight into ways to correctly
implement the technique when the base flow comes from RANS.
Finally, the dynamics of the swept interaction are explored to characterize its unsteady
and stability features. Here the basic state is obtained by tailoring RANS calculations to
experiments at Florida State University, allowing the separation and other relevant mean
features to be accurately captured. The flow field obtained by perturbing this mean is post
processed to identify the length and time scales relevant to the flow field.
This effort accomplishes three things: (i) a tripping technique is generated to efficiently specify turbulent boundary layer appropriate for use as the inflow condition, (ii) LES of 2-D interactions are obtained and analyzed to identify the cause of energetic low frequency and (iii) the relevant frequencies in the swept interaction are characterized using MFP and the stability properties of the interaction are identified, distinguishing its dynamics from the 2-D. Each step involves a myriad of statistical tools that can be adapted for other applications. The findings of each effort are presented.
It is found that the effectiveness of tripping a laminar boundary layer to yield its turbulent counterpart is dependent on a range of factors: (i) grid resolution, (ii) strength of the force associated with the trip, (iii) wall thermal condition near the trip and (iv) Mach number. By characterizing the stability of the boundary layer in the trip region, a precursor for transition to turbulence is identified. This makes the method efficient for generating turbulent boundary layers at alternative desired flow conditions (Mach and Reynolds numbers) as appropriate trip parameters can be obtained a priori.
Statistical analyses of the shock motions in 2-D interactions reveal an asymmetry whose quality appears to be dependent on the separation bubble size. For massive separation bubbles, where the shear layer is detached, the collapse phase is a rapid process, possibly owing to the ease of formation of Kelvin-Helmholtz (K-H) structures which convect mass and momentum out of the bubble, leading to its collapse. For moderate separation bubbles, the collapse phase is instead the slower process. It is found that the quality of the asymmetry is linked to the linearly stable position of the shock, which has implications for control. In addition, there is evidence of modulation of the frequencies associated with K-H shedding by the low frequencies characteristic of the shock motions, establishing a link between the two physical phenomena and further reinforcing the role of eddies in bubble collapse.
The most substantial outcome of this work is the insight obtained regarding the dynamics of the swept interaction. The results show that: (i) The shock generated by the fin is anchored unlike the oscillating reflected shock in 2-D; consequently, the low frequencies observed in 2-D are not present in this swept interaction. (ii) A convective inviscid instability is identified at a frequency an order of magnitude higher than the characteristic frequency of shock motions in 2-D. It is shown to be a consequence of the crossflow and analogous to the mid frequencies associated with K-H shedding in the 2-D interaction. (iii) The absolute instability observed in 2-D does not persist here as the absence of a closed separation reduces the interaction’s ability to perpetually self-sustain introduced perturbations. |